Slide drilling is widely used in directional drilling because of its lower cost, but the tool-face adjustment during the drilling process is almost completed by the driller, and the automatic control has not yet been realized. The main difficulty is that the drill string system has a large amount of contact and friction with the wellbore. Moreover, it is also affected by the viscous force of the mud fluid, which brings more difficulty to achieve accurate dynamic model. Considering that the actual drilling is too costly, it is necessary to establish an indoor experimental system to simulate the response of the slide drilling tool-face, thus providing an experimental platform for the research of the control method. In this paper, the dynamic equation of the torsion process of the drill pipe is established. According to the model similarity theory, the similarity condition of parameters and scale correspondence between the experimental model and the drilling prototype are obtained, which provides the basis for selection of simulated drill pipe and mud. Then the expert PID method is used to realize the automatic tool-face control based on the laboratory experimental system. The experimental results show that the expert PID method can obtain better control effect rather than the traditional PID method, and it could be used in the actual slide drilling because of the dynamic similarity.